Bayes' theorem with ​2​ and ​3​ events, sum of conditional probabilities
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Bayes' theorem allows us to reverse conditional probabilities, determining the probability of an event based on prior knowledge of another event. If we have events ​A​ and ​B, Bayes' theorem states:
In other words, Bayes' theorem lets us update our beliefs or predictions after observing new evidence. It's particularly useful when dealing with sequential information or adjusting probabilities based on new data.
In some cases, instead of complementary events ​B​ and ​B′, we have complementary events ​B1​, ​B2​​ and ​B3​. In this case Bayes' theorem can be generalized to